On the determination of the control parameters of the optimal can-order policy

This paper considers the well-known class of can-order policies. This type of coordinated replenishment policies accounts for a joint set-up cost structure, where a major set-up cost is incurred for any order and an individual minor set-up cost is charged for each item in the replenishment. Recent comparative studies have pointed out that the performance of the optimal can-order policy is poor, compared to other coordinated replenishment strategies, when the major set-up cost is high. This paper shows that it is the approximate decomposition method to calculate the optimal canorder parameters which performs bad in such situations and not the policy itself. Attention is focused to a subclass of can-order policies, which is close to the optimal can-order policy for high major set-up costs. A solution procedure is developed to calculate the optimal control parameters of this policy. It is shown that a properly chosen combination of the solution procedures to calculate can-order parameters leads to a can-order strategy which performs as well as other coordinated replenishment policies.     

A quantitative approach for scheduling activities to reduce set-up in multiple machine lines

The importance of ensuring short set-up times in manufacturing has been well-documented in the literature over the past years. However, this body of work largely addresses situations involving a single machine with no specific worker-related issues. In practice, there exist multiple machines or workstations that form a machine line, and that need set-up operations to be performed by multiple workers. The existing literature does not provide adequate methodologies for set-up reduction in such cases. This paper describes a quantitative modeling and algorithmic approach for scheduling activities or tasks in order to minimize the set-up time in such situations, also taking into account relevant secondary objectives such as balancing the workload amongst the workers, concentrating slack toward the end of the set-up process, and minimizing the movement costs of the workers performing the different set-up tasks. Three real-life examples are used to demonstrate the efficacy of the proposed approach.     

Single-machine scheduling of multi-operation jobs without missing operations to minimize the total completion time

We consider the problem of scheduling multi-operation jobs on a singe machine to minimize the total completion time. Each job consists of several operations that belong to different families. In a schedule each family of job operations may be processed as batches with each batch incurring a set-up time. A job is completed when all of its operations have been processed. We first show that the problem is strongly NP-hard even when the set-up times are common and each operation is not missing. When the operations have identical processing times and either the maximum set-up time is sufficiently small or the minimum set-up time is sufficiently large, the problem can be solved in polynomial time. We then consider the problem under the job-batch restriction in which the operations of each batch is partitioned into operation batches according to a partition of the jobs. We show that this case of the problem can be solved in polynomial time under a certain condition.     

Joint Replenishment in Multi-Item Inventory Systems

A multi-item inventory system is considered which has the property that, for each single item, a reorder policy using the E.O.Q. formula would be appropriate. Holding costs are linear, and fixed ordering costs are assumed to be composed of a major set-up cost reflecting the pure fact of placing an order, and a sum of minor set-up costs corresponding to the items included in the order. If it is desirable to form a certain number of groups of items where all items of one group share the same order cycle, it is shown that there is always an optimal grouping in which items are arranged in increasing order of their ratio of yearly holding costs and minor set-up costs.A heuristic for forming the groups is given which turns out to be an optimal algorithm for the case that there are no major set-up costs. After an initial sorting of ratios, the worst-case complexity of this procedure is linear in the number of items.     

A New Heuristic for a Single Machine Scheduling Problem with Set-up Times

This paper examines the problem of scheduling jobs on a single machine with set-up times. The jobs are divided into mutually exclusive classes and a set-up task is required when processing switches from a job of one class to a job of another class. The set-up times are assumed to be sequence independent. A number of necessary conditions for a schedule to minimize mean flow time have previously been stated, but do not uniquely define the optimal solution, and the problem is apparently NP-complete. We propose a new polynomial-time heuristic, based on these conditions, and compare its performance with some existing heuristics.     

An effective heuristic for the CLSP with set-up times

The problem of multi-item, single level, capacitated, dynamic lot-sizing with set-up times (CLSP with set-up times) is considered. The difficulty of the problem compared with its counterpart without set-up times is explained. A lower bound on the value of the objective function is calculated by Lagrangian relaxation with subgradient optimisation. During the process, attempts are made to get good feasible solutions (ie. upper bounds) through a smoothing heuristic, followed by a local search with a variable neighbourhood. Solutions found in this way are further optimised by solving a capacitated transshipment problem. The paper describes the various elements of the solution procedure and presents the results of extensive numerical experimentation.     

A tabu search heuristic for solving the CLSP with backlogging and set-up carry-over

In this paper, the multi-item, single-level, capacitated, dynamic lot sizing problem with set-up carry-over and backlogging, abbreviated to CLSP⁺, is considered. The problem is formulated as a mixed integer programming problem. A heuristic method consisting of four elements: (1) a demand shifting rule, (2) lot size determination rules, (3) checking feasibility conditions and (4) set-up carry-over determination, provides us with an initial feasible solution. The resulting feasible solution is improved by adopting the corresponding set-up and set-up carry-over schedule and re-optimizing it by solving a minimum-cost network flow problem. Then the improved solution is used as a starting solution for a tabu search procedure, with the value of moves assessed using the same minimum-cost network problem. Computational results on randomly generated problems show that the algorithm, which is coded in C++, is able to provide optimal solutions or solutions extremely close to optimal. The computational efficiency makes it possible to solve reasonably large problem instances routinely on a personal computer.     

Economic Packaging Frequency of Jointly Replenished Items having Interdependent Packaging Set-up Cost

The method described in this paper is applicable to the batch processing industry where a batch of a product is packaged into several container sizes immediately after manufacture. A packaging set-up is required whenever the unpackaged product is packaged into a particular packaging size, and the packaging set-up cost for each size depends on the preceding size packaged. An example involving four packaging sizes has been solved to illustrate the method.     

Balancing capacity and lot sizes

In many companies there is an on-going discussion about capacity, capacity utilization and capital tied up in inventories. However, traditional models such as the EOQ model only include capacity considerations in the set-up cost, or in the cost of a replenishment order. This implies e.g. that they do not consider the set-up time as a capacity constraint. Furthermore, in these models the set-up cost is usually treated as a constant, even though the opportunity cost for capacity in general is dependent upon the capacity utilization.The purpose of this paper is to derive an analytical model for the balancing of capacity and lot sizes. The model includes costs for capacity, work-in-process (queueing, set-up, and processing time), and finished goods inventory. The total costs are minimized with respect to capacity. Then, the corresponding, recommended lot sizes are determined. The model was tested with data from a Swedish manufacturing company. The results turned out to coincide with experiences of the company in many important respects. The model offers production management an opportunity to discuss the relationship between capacity, work-in-process, and lot sizes.     

On the Stochastic Non-sequential Production-planning Problem

This paper examines a stochastic non-sequential capacitated production-planning problem where the demand of each period is a continuous random variable. The stochastic non-sequential production-planning problem is examined with sequence-independent and then with sequence-dependent set-up costs, and the worst-case error determined when an approximate solution is obtained by solving the deterministic equivalent. We prove in general that the worst-case error is not dependent on the nature of the set-up cost, and identify a family of approximations for the stochastic non-sequential production-planning problem.     

Multi-item lot-sizing with joint set-up costs

We consider a multi-item lot-sizing problem with joint set-up costs and constant capacities. Apart from the usual per unit production and storage costs for each item, a set-up cost is incurred for each batch of production, where a batch consists of up to C units of any mix of the items. In addition, an upper bound on the number of batches may be imposed. Under widely applicable conditions on the storage costs, namely that the production and storage costs are nonspeculative, and for any two items the one that has a higher storage cost in one period has a higher storage cost in every period, we show that there is a tight linear program with O(mT ²) constraints and variables that solves the joint set-up multi-item lot-sizing problem, where m is the number of items and T is the number of time periods. This establishes that under the above storage cost conditions this problem is polynomially solvable. For the problem with backlogging, a similar linear programming result is described for the uncapacitated case under very restrictive conditions on the storage and backlogging costs. Computational results are presented to test the effectiveness of using these tight linear programs in strengthening the basic mixed integer programming formulations of the joint set-up problem both when the storage cost conditions are satisfied, and also when they are violated.     

An inventory system with investment to reduce yield variability and set-up cost

The set-up cost and yield variability are given and fixed in existing production/inventory models with random yields. However, in many practical situations, they can be reduced by investment in modern production technology. In this paper, we consider an inventory system with random yield in which both the set-up cost and yield variability can be reduced through capital investment. The objective is to determine the optimal capital investment and ordering policies that minimize the expected total annual costs for the system. In addition, an iterative solution procedure is presented to find the optimal order quantity and reorder point and then the optimal set-up cost and yield standard deviation. Numerical examples are given to illustrate the results obtained and assess the cost savings by adopting capital investments. Managerial implications are also included.     

Solving the discrete lotsizing and scheduling problem with sequence dependent set-up costs and set-up times using the Travelling Salesman Problem with time windows

In this paper we consider the Discrete Lotsizing and Scheduling Problem with sequence dependent set-up costs and set-up times (DLSPSD). DLSPSD contains elements from lotsizing and from job scheduling, and is known to be NP-Hard. An exact solution procedure for DLSPSD is developed, based on a transformation of DLSPSD into a Travelling Salesman Problem with Time Windows (TSPTW). TSPTW is solved by a novel dynamic programming approach due to Dumas et al. (1993). The results of a computational study show that the algorithm is the first one capable of solving DLSPSD problems of moderate size to optimality with a reasonable computational effort.     

Optimal strategy in <Emphasis Type="Italic">N</Emphasis>-policy production system with early set-up

This paper considers a production system in which an early set-up is possible. The machine(server) is turned off when there are no units(customers) to process. When the accumulated number of units reaches m(<N), the operator starts a set-up that takes a random time. After the set-up, if there are N or more units waiting for processing, the machine begins to process the units immediately. Otherwise the machine remains dormant in the system until the accumulated number of units reaches N. We model this system by M/G/1 queue with early set-up and N-policy. We use the decomposition property of a vacation queue to derive the distribution of the number of units in the system. We, then, build a cost model and develop a procedure to find the optimal values of (m,N) that minimize a linear average cost.     

Evaluation of scheduling algorithms for resources with high set-up time

Tapes and removable disks are considered resources with high set-up time. When dealing with such resources, a simple and apparently appealing heuristics consists of scheduling jobs to minimize the total number of set-up. In this paper, we examine the validity of such approach, developing both a probabilistic and a simulation model. For sake of concreteness, the example considered refers to a system consisting of a tape library and a limited number of drives. The results obtained are discussed and the problem of applying the proposed evaluation technique to computer centers with different library frequency distributions is examined.     

多重休假的带启动--关闭期的Geom/G/1排队

本研究多重休假的带启动——关闭期的Geom／G／1离散时间排队，给出稳态队长，等待时间分布的母函数及其随机分解结果，推导出忙期的全假期的母函数，给出该模型的几个特例。     

A TSP (1,2) application arising in cable assembly shops

One of the main operations in producing cable systems in the automotive industry is that of cutting/stripping/crimping. The most time-consuming activity in this operation is changing the heads whenever a different connector is to be crimped at either one of the ends. This set-up time is practically doubled when the heads at both ends are to be changed. Thus, one is faced with the problem of minimizing the total machine set-up time; which turns out to be a TSP where the distances between the nodes are either one or two. A simple and effective heuristic algorithm is developed that yields solutions, which are only a few percent above the optimum in the worst case.     

Duality results for extended multifacility location problems

Abstract

Duality statements are presented for multifacility location problems as suggested by Drezner Hiu 1991, where for each given point the sum of weighted distances to all facilities plus set-up costs is determined and the maximal value of these sums is to be minimized. We develop corresponding dual problems for the cases with and without set-up costs and present associated optimality conditions. In the concluding part of this note we use these optimality conditions for a geometrical characterization of the set of optimal solutions and consider for an illustration corresponding examples.     

有优先权顾客带启动时间多重休假的M~(1)+M~(2)/G/1排队系统

研究了带启动时间有顾客优先权多重休假的M(1)+M(2)/G/1排队系统,分别给出了两类顾客的稳态队长的母函数和等待时间分布的LST及其随机分解的结果,推导出忙期、假期和启动期的LST等.